# Computational Mechanics

## ME 3255 (FA 2016)

Class Number: **2733**

TuTh 11:00AM – 12:15PM Laurel Hall 201

Topics include elementary numerical analysis, finite differences, initial value problems, ordinary and partial differential equations, and finite element techniques. Applications include structural analysis, heat transfer, and fluid flow.

# Principles of Optimal Design

## ME 5511 (FA 2015)

In this course we study the application of mathematical optimization concepts to the numerical solution of engineering design problems. We also examine heuristic methods for the solution of optimization problems for which efficient gradient-based solution methods cannot be used. We will briefly cover the use of Excel and Matlab to solve optimization problems; however,the focus of the class is not on the tools but on understanding the underlying concepts behind optimal design in order to make intelligent use of these tools (and others that you may encounter throughout your career). This understanding includes identifying when and how to cast a design problem into an optimization problem, how to choose the most (or *an*) appropriate algorithm to solve it, how to interpret the results of the optimization, and how to diagnose problems when things go wrong.

# Design with the Finite Element Method

## ME 5895 Special Topics in Mechanical Engineering (SP 2015, SP 2016, FA 2017)

In this course, we study the derivation of design sensitivities of structures modeled via the finite element method, which can be used in conjunction with nonlinear programming algorithms for the design of the structure. In particular, we will study the mathematical derivation and computational implementation of material and shape sensitivities of linear elastostatic systems that can be used for shape and topology optimization.

At the end of this class you should be able to compute analytical and numerical design sensitivities so that changes in the system response with respect to changes in the design can be quantified in a computationally efficient manner. In particular, you should be able to apply the direct and adjoint sensitivity methods, distinguishing the computational advantages of each, and then use these sensitivities with gradient-based optimizers to design the structure.